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<span class="breadcrumb-node">Serial Differencing Aggregation</span>
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<div class="section">
<div class="titlepage"><div><div>
<h2 class="title">
<a id="search-aggregations-pipeline-serialdiff-aggregation"></a>Serial Differencing Aggregation<a class="edit_me edit_me_private" rel="nofollow" title="Editing on GitHub is available to Elastic" href="https://github.com/elastic/elasticsearch/edit/7.7/docs/reference/aggregations/pipeline/serial-diff-aggregation.asciidoc">edit</a>
</h2>
</div></div></div>
<p>Serial differencing is a technique where values in a time series are subtracted from itself at
different time lags or periods. For example, the datapoint f(x) = f(x<sub>t</sub>) - f(x<sub>t-n</sub>), where n is the period being used.</p>
<p>A period of 1 is equivalent to a derivative with no time normalization: it is simply the change from one point to the
next. Single periods are useful for removing constant, linear trends.</p>
<p>Single periods are also useful for transforming data into a stationary series. In this example, the Dow Jones is
plotted over ~250 days. The raw data is not stationary, which would make it difficult to use with some techniques.</p>
<p>By calculating the first-difference, we de-trend the data (e.g. remove a constant, linear trend).  We can see that the
data becomes a stationary series (e.g. the first difference is randomly distributed around zero, and doesn’t seem to
exhibit any pattern/behavior). The transformation reveals that the dataset is following a random-walk; the value is the
previous value +/- a random amount.  This insight allows selection of further tools for analysis.</p>
<div id="serialdiff_dow" class="imageblock">
<div class="content">
<img src="images/pipeline_serialdiff/dow.png" alt="dow">
</div>
<div class="title">Figure 17. Dow Jones plotted and made stationary with first-differencing</div>
</div>
<p>Larger periods can be used to remove seasonal / cyclic behavior. In this example, a population of lemmings was
synthetically generated with a sine wave + constant linear trend + random noise. The sine wave has a period of 30 days.</p>
<p>The first-difference removes the constant trend, leaving just a sine wave. The 30th-difference is then applied to the
first-difference to remove the cyclic behavior, leaving a stationary series which is amenable to other analysis.</p>
<div id="serialdiff_lemmings" class="imageblock">
<div class="content">
<img src="images/pipeline_serialdiff/lemmings.png" alt="lemmings">
</div>
<div class="title">Figure 18. Lemmings data plotted made stationary with 1st and 30th difference</div>
</div>
<div class="section">
<div class="titlepage"><div><div>
<h3 class="title">
<a id="_syntax_14"></a>Syntax<a class="edit_me edit_me_private" rel="nofollow" title="Editing on GitHub is available to Elastic" href="https://github.com/elastic/elasticsearch/edit/7.7/docs/reference/aggregations/pipeline/serial-diff-aggregation.asciidoc">edit</a>
</h3>
</div></div></div>
<p>A <code class="literal">serial_diff</code> aggregation looks like this in isolation:</p>
<div class="pre_wrapper lang-js">
<pre class="programlisting prettyprint lang-js">{
    "serial_diff": {
        "buckets_path": "the_sum",
        "lag": "7"
    }
}</pre>
</div>
<div class="table">
<a id="serial-diff-params"></a>
<p class="title"><strong>Table 29. <code class="literal">serial_diff</code> Parameters</strong></p>
<div class="table-contents">
<table border="1" cellpadding="4px" summary="serial_diff Parameters">
<colgroup>
<col class="col_1">
<col class="col_2">
<col class="col_3">
<col class="col_4">
</colgroup>
<thead>
<tr>
<th align="left" valign="top">Parameter Name</th>
<th align="left" valign="top">Description</th>
<th align="left" valign="top">Required</th>
<th align="left" valign="top">Default Value</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top"><p><code class="literal">buckets_path</code></p></td>
<td align="left" valign="top"><p>Path to the metric of interest (see <a class="xref" href="search-aggregations-pipeline.html#buckets-path-syntax" title="buckets_path Syntax"><code class="literal">buckets_path</code> Syntax</a> for more details</p></td>
<td align="left" valign="top"><p>Required</p></td>
<td align="left" valign="top"><p></p></td>
</tr>
<tr>
<td align="left" valign="top"><p><code class="literal">lag</code></p></td>
<td align="left" valign="top"><p>The historical bucket to subtract from the current value. E.g. a lag of 7 will subtract the current value from
 the value 7 buckets ago. Must be a positive, non-zero integer</p></td>
<td align="left" valign="top"><p>Optional</p></td>
<td align="left" valign="top"><p><code class="literal">1</code></p></td>
</tr>
<tr>
<td align="left" valign="top"><p><code class="literal">gap_policy</code></p></td>
<td align="left" valign="top"><p>Determines what should happen when a gap in the data is encountered.</p></td>
<td align="left" valign="top"><p>Optional</p></td>
<td align="left" valign="top"><p><code class="literal">insert_zero</code></p></td>
</tr>
<tr>
<td align="left" valign="top"><p><code class="literal">format</code></p></td>
<td align="left" valign="top"><p>Format to apply to the output value of this aggregation</p></td>
<td align="left" valign="top"><p>Optional</p></td>
<td align="left" valign="top"><p><code class="literal">null</code></p></td>
</tr>
</tbody>
</table>
</div>
</div>
<p><code class="literal">serial_diff</code> aggregations must be embedded inside of a <code class="literal">histogram</code> or <code class="literal">date_histogram</code> aggregation:</p>
<div class="pre_wrapper lang-console">
<pre class="programlisting prettyprint lang-console">POST /_search
{
   "size": 0,
   "aggs": {
      "my_date_histo": {                  <a id="CO275-1"></a><i class="conum" data-value="1"></i>
         "date_histogram": {
            "field": "timestamp",
            "calendar_interval": "day"
         },
         "aggs": {
            "the_sum": {
               "sum": {
                  "field": "lemmings"     <a id="CO275-2"></a><i class="conum" data-value="2"></i>
               }
            },
            "thirtieth_difference": {
               "serial_diff": {                <a id="CO275-3"></a><i class="conum" data-value="3"></i>
                  "buckets_path": "the_sum",
                  "lag" : 30
               }
            }
         }
      }
   }
}</pre>
</div>
<div class="console_widget" data-snippet="snippets/584.console"></div>
<div class="calloutlist">
<table border="0" summary="Callout list">
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO275-1"><i class="conum" data-value="1"></i></a></p>
</td>
<td align="left" valign="top">
<p>A <code class="literal">date_histogram</code> named "my_date_histo" is constructed on the "timestamp" field, with one-day intervals</p>
</td>
</tr>
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO275-2"><i class="conum" data-value="2"></i></a></p>
</td>
<td align="left" valign="top">
<p>A <code class="literal">sum</code> metric is used to calculate the sum of a field.  This could be any metric (sum, min, max, etc)</p>
</td>
</tr>
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO275-3"><i class="conum" data-value="3"></i></a></p>
</td>
<td align="left" valign="top">
<p>Finally, we specify a <code class="literal">serial_diff</code> aggregation which uses "the_sum" metric as its input.</p>
</td>
</tr>
</table>
</div>
<p>Serial differences are built by first specifying a <code class="literal">histogram</code> or <code class="literal">date_histogram</code> over a field.  You can then optionally
add normal metrics, such as a <code class="literal">sum</code>, inside of that histogram.  Finally, the <code class="literal">serial_diff</code> is embedded inside the histogram.
The <code class="literal">buckets_path</code> parameter is then used to "point" at one of the sibling metrics inside of the histogram (see
<a class="xref" href="search-aggregations-pipeline.html#buckets-path-syntax" title="buckets_path Syntax"><code class="literal">buckets_path</code> Syntax</a> for a description of the syntax for <code class="literal">buckets_path</code>.</p>
</div>

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